Time: 10:30-11:30 January 16, 2025 (Thursday)
Venue: MCM110
Title: Orbit closures in flag varieties for the centralizer of an order-two nilpotent element: normality and resolutions for types A, B, D.
Abstract: Let $G$ be a reductive algebraic group in classical types A, B, D and $e$ be a nilpotent element of its Lie algebra, with centralizer $Z$. We assume being in the two columns case. We show that any $Z$-orbit closure in the flag variety of $G$ is normal. For this purpose, we exhibit a birational, rational morphism built on Schubert varieties and symmetric subgroups. We also use a Frobenius splitting theorem due to X.He and J.F.Thomsen, and an inductive result inspired by M.Brion and S.Kumar, developped by N.Perrin and E.Smirnov.
